Problem: What is $75\%$ of $200$ ?
Solution: Having $75\%$ of something means that you get $75$ out of every $100$ We can set up a proportion to find out what number is $75\%$ of $200$ $ \dfrac{{\text{percent}}}{100} = \dfrac{{\text{part}}}{{\text{whole}}}$ Which things do we know, and what are we trying to find? We know the ${\text{percent}}$ is $75$ . Is $200$ the ${\text{part}}$ or the ${\text{whole}}$ The $200$ is the ${\text{whole}}$ . We are trying to find the ${\text{part}}$ that makes up $75\%$ of it: $ \dfrac{{75}}{100} = \dfrac{{\text{part}}}{{200}}$ If we multiply the denominator of the fraction on the left by $2$ , it will be the same denominator of the fraction on the right. To keep things equal, let's also multiply the numerator on the left by $2$ $ \dfrac{{75} \times 2}{100 \times 2} = \dfrac{{\text{part}}}{{200}}$ $ \dfrac{{150}}{200} = \dfrac{{\text{part}}}{{200}}$ $ {150} = {\text{part}}$ So $150$ is $75\%$ of $200$.